A variety of photoelectric, magnetic, inductive and capacitive measuring systems are known to the art for measuring the relative position of two objects, such as the relative position between a slide piece and a bed of a machine tool, for example. While there are distinctions between photoelectric, magnetic, inductive and capacitive scanning, all methods have a common basic principle, a periodic graduation is scanned and the scanning signal generated in this way is evaluated as the measuring signal.
In the case of prior art photoelectric length measuring systems, a measuring scale which defines a periodic graduation is mounted to a first object and this scale is scanned by a scanning unit which is connected with a second object. The scanning unit includes for this purpose an illuminating system and a scanning plate which may, for example, include two graduation fields. The graduations of these fields are typically offset with respect to one another by a phase angle of 90.degree. and correspond precisely in period with the graduation of the measuring scale. In addition, the scanning unit includes, for example, two photosensors, each of which is associated with a respective one of the graduation fields.
In the case of transmitted light measuring systems, the similar graduations on the scanning plate and the measuring scale are made up of alternating photopermeable and photoimpermeable strips which alternate along the longitudinal extent of the measuring scale (the measuring direction).
The light flux generated by the illumination system passes through the graduations of the measuring scale and the scanning plate and then falls upon the photosensors. Thus, the light falling on the photosensors is modulated by the relative movement of the scanning plate with respect to the measuring scale. The two photosensors associated with respective ones of the graduation fields generate two periodic electric analog signals which are phase shifted with respect to one another by a phase angle of 90.degree. and are sinusoidal in wave form. These sinusoidal analog signals are applied as inputs to an evaluating arrangement which determines the measured position value from the analog signals. The period of the analog signals generated by the scanning unit is determined by the period of the graduation of the measuring scale. This period is in turn determined by the width of the alternating photopermeable and photoimpermeable strips along the measuring direction. In relative movement between the scanning unit and the measuring scale, each period of the graduation of the measuring scale results in the generation of a counting pulse which is counted and displayed.
In general, the periodic analog signals obtained from the graduations of a measuring scale in photoelectric, magnetic, inductive, and capacitive measuring systems are not precisely sinusoidal in wave form. Rather, in general, such periodic analog signals include harmonic components as a consequence of inaccuracies in the graduations. Such inaccuracies can result, for example, from differing spacings between the photopermeable and the photoimpermeable strips of the graduations, or by an edge blurring of these strips.
One prior art approach to minimize the harmonic components in the analog scanning signal is to place high precision demands on the accuracy of the graduation. If the periodic analog signals are to be used to form exact position measuring values for each graduation period and to provide improved measuring precision by subdividing the graduation periods of the graduation through the formation of interpolation values, the analog signals obtained from the graduation must be substantially free of harmonics. The prior art discloses several approaches to the formation of such interpolation values, such as the computer based approach described in U.S. Pat. No. 4,225,931 which is specifically incorporated herein by reference.
In addition to the measuring systems described above, other classes of prior art measuring systems generate triangular or trapezoidal analog measuring signals, which by their very nature include a large harmonic component.
U.S. Pat. No. 3,674,372 which is specifically incorporated herein by reference discloses a photoelectric length measuring system in which harmonic components in the analog signal generated in the scanning of the graduation of the measuring scale are reduced by means of a frequency filter diaphragm having a sinusoidal permeability characteristic. In this measuring system it is necessary for a special frequency filter diaphragm to be produced and installed on the measuring system. Moreover, this approach to the reduction of harmonic components is restricted to use in photoelectric measuring systems which operate according to the transmitted light measuring principle.
U.S. Pat. No. 4,595,991 which is specifically incorporated herein by reference discloses a position measuring system and method for generating harmonic-free periodic signals of the type comprising a measuring scale which includes a periodic graduation and a scanning unit adapted to scan the measuring scale with at least 2N scanning elements. Each of the scanning elements is included in the scanning unit to scan the periodic graduation and to generate a respective periodic scanning signal in response thereto. The number of scanning elements is selected at twice the bandwidth N of the scanning signals generated by the scanning elements. A Fourier analysis is performed on the scanning signals to determine a pair of Fourier coefficients characteristic of the fundamental component of the scanning signals. These Fourier coefficients are evaluated as substantially harmonic-free periodic signals to determine the position of the scanning unit with respect to the measuring scale.
U.S. Pat. No. 4,602,436 which is specifically incorporated herein by reference discloses a measuring system in which harmonic-free periodic signals are recovered, which does not require special optical elements and which can be used in direct light and in reflected light measuring systems. The position measuring system is provided with at least two first scanning fields included in the scanning unit, offset with respect to one another along the measuring direction. Each scanning field comprises N partial fields, where N is the bandwidth of the periodic analog signal. Adjacent partial fields are displaced with respect to one another by a constant dimension in the measuring direction, and each of the partial fields defines a respective width along the measuring direction. The widths of the partial fields vary according to a sine function. In addition, means are provided for developing first periodic signals from the partial fields and for superposing the first periodic signals to generate a harmonic-free periodic analog signal. Alternatively, the scanning fields each define respective scanning field midlines and the scanning field midlines are offset with respect to one another along the measuring direction. Each scanning field comprises M partial fields where M is greater than or equal to N. These partial fields are positioned such that the separation in the measuring direction between the partial field midlines and the scanning field midlines varies according to an arcsin function and each of the partial fields defines a constant width.
Many of these methods, for example, Vernier, Vernier-arcsin or multi-field filtering are based on a special scanning graduation. The grating line positions X.sub.n (where n is the grating line index of the scanning graduation) are respectively displaced by a small amount .delta..sub.n in relation to the nominal position defined as n.multidot.P where P is the graduation period of the measuring scale. The grating line positions can be defined by the equation X.sub.n =n.multidot.P+.delta..sub.n. These displacements .delta..sub.n of the grating line positions of the scanning graduation cause a phase shift of the associated signal portion and are selected such that, in the superposition of all signal portions, individual or all harmonics are substantially suppressed. The various methods for harmonic filtering based on this principle have different functional dependencies between the displacement .delta..sub.n and the grating line index n. For example, for a Vernier filter, .delta..sub.n can be defined by the equation .delta..sub.n =n.multidot..alpha..multidot.P, where .alpha.&lt;&lt;1. For an arcsin filter, .delta..sub.n can be defined by the equation .delta..sub.n =P/2.pi..multidot.arcsin (n/N), where n=-N . . . +N.
A constant increase or decrease of the displacement .delta..sub.n with an increasing grating line index n is common to all these methods. The result of this is that signal portions with a larger phase difference are generated at scanning positions which are far apart from each other. Thus a noticeable filtering effect is only assured if the signal portions of a relatively large scanning region are superimposed evenly and without interference. However, interferences occur frequently in actuality which greatly impair the filtering effects. Such interferences result from uneven intensity of illumination within the scanning graduation, illumination of the scanning graduation by a decollimated (divergent or convergent) light beam and local flaws in the scanning or scale graduation, for example.
These interferences not only reduce the filtering effect, they also displace the phase relation of the signal composed of the individual phase-shifted portions thereby further reducing signal quality.